Estimating basin-averaged erosion rates from cosmogenic nuclide concentrations in sediment from landslide-dominated drainage basins

Recent employment of cosmogenic radionuclides (CRN) has allowed the determination of basin-average denudation rates but is restricted to basins in which the erosion rate is steady. We discuss the theoretical basis for extending this method to areas prone to landslides, in which the sediment delivery rate to the channel is highly variable in both time and space. We use a simple 1-D model of the depth-dependent nuclide concentration profile to estimate the variation in erosion rates calculated from CRN concentrations in fluvial sediments delivered by landslide processes. We explore four scenarios: (1) depth of landslide and return interval are held constant; (2) depth of landslide is held constant and return interval is stochastic following a uniform distribution; (3) return interval is constant and depth of landslide is stochastic following a power law distribution; and (4) depth of landslide and return interval are stochastic. In addition, we explore various power law distributions, erosion rates, and contributions from steady, background erosion processes. Cosmogenic nuclide concentration and mass of the eroded material is tracked through time. Relative to previously derived analytical solutions for estimation of erosion rates from CRN concentrations in alluvial sediment, we predict that CRN concentrations in landslide-dominated drainage basins can either underestimate or overestimate the mean physical mass removal rates. Both effects are more pronounced under a heavy-tailed landslide magnitude-frequency distribution. Overestimation can occur when sediment from a large, rare event dominates the fluvial sample. On the other hand, if the largest landslides dominate the sediment budget, underestimation of denudation rate can occur when the sediment is sampled during the long interval between these events and consists mostly of material derived from smaller landslides and/or steady hillslope processes. The degree of miscalculation will depend on the relative contribution of steady background erosion processes, the variability in the landslide magnitude-frequency distribution, and the space and time scales of sediment mixing in the fluvial system. To explore further the issue of spatial and temporal sediment mixing, we present initial results from a 2-D model of an entire drainage basin subject to landslides. We discuss various means of correcting CRN-based estimates of mean erosion rates in systems prone to landslides.